The National Task Force on Organ Transplantation recommended developing methods to increase transplantation of the highly sensitized patient. We, and others, have shown that patients can be successfully transplanted with a current negative/past positive crossmatch after a spontaneous fall in antibody titer. We, and others, have shown that ABO incompatible transplants can be successfully done after antibody removal. Recently it has been demonstrated that: a) renal transplants can be done after removing (by plasmapheresis or immunoadsorption) anti-HLA antibody and preventing antibody return with immunosuppression, and b) that short-term immunosuppression results in a fall in anti-HLA antibody titer. In this study, we will determine whether immunosuppression will safely provide long-term reduction in antibody titer. Pre-immunosuppression PRA will be compared with post-immunosuppression PRA by paired T tests. We will determine if immunosuppression is equally effective in patients with high titers of one or two anti-HLA antibodies which crossreact with other HLA antigens, and in patients with broadly reactive antibodies. We will learn whether candidates in each of the groups where PRA falls with immunosuppression can be successfully transplanted with a donor organ to which the patient has a past positive crossmatch.